44 research outputs found
Phase behavior of polydisperse sticky hard spheres: analytical solutions and perturbation theory
We discuss phase coexistence of polydisperse colloidal suspensions in the
presence of adhesion forces. The combined effect of polydispersity and Baxter's
sticky-hard-sphere (SHS) potential, describing hard spheres interacting via
strong and very short-ranged attractive forces, give rise, within the
Percus-Yevick (PY) approximation, to a system of coupled quadratic equations
which, in general, cannot be solved either analytically or numerically. We
review and compare two recent alternative proposals, which we have attempted to
by-pass this difficulty. In the first one, truncating the density expansion of
the direct correlation functions, we have considered approximations simpler
than the PY one. These approximations can be systematically improved.
We have been able to provide a complete analytical description of polydisperse
SHS fluids by using the simplest two orders and , respectively.
Such a simplification comes at the price of a lower accuracy in the phase
diagram, but has the advantage of providing an analytical description of
various new phenomena associated with the onset of polydispersity in phase
equilibria (e.g. fractionation). The second approach is based on a perturbative
expansion of the polydisperse PY solution around its monodisperse counterpart.
This approach provides a sound approximation to the real phase behavior, at the
cost of considering only weak polydispersity. Although a final seattlement on
the soundness of the latter method would require numerical simulations for the
polydisperse Baxter model, we argue that this approach is expected to keep
correctly into account the effects of polydispersity, at least qualitatively.Comment: 12 pages, 4 figures, to appear in Molec. Phys. special issue Liblice
200
On the compressibility equation of state for multicomponent adhesive hard sphere fluids
The compressibility equation of state for a multicomponent fluid of particles
interacting via an infinitely narrow and deep potential, is considered within
the mean spherical approximation (MSA). It is shown that for a class of models
leading to a particular form of the Baxter functions containing
density-independent stickiness coefficient, the compressibility EOS does not
exist, unlike the one-component case. The reason for this is that a direct
integration of the compressibility at fixed composition, cannot be carried out
due to the lack of a reciprocity relation on the second order partial
derivatives of the pressure with respect to two different densities. This is,
in turn, related to the inadequacy of the MSA. A way out to this drawback is
presented in a particular example, leading to a consistent compressibility
pressure, and a possible generalization of this result is discussed.Comment: 13 pages, no figures, accepted for publication Molec. Physics (2002
Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles
We study the polydisperse Baxter model of sticky hard spheres (SHS) in the
modified Mean Spherical Approximation (mMSA). This closure is known to be the
zero-order approximation (C0) of the Percus-Yevick (PY) closure in a density
expansion. The simplicity of the closure allows a full analytical study of the
model. In particular we study stability boundaries, the percolation threshold,
and the gas-liquid coexistence curves. Various possible sub-cases of the model
are treated in details. Although the detailed behavior depends upon the
particularly chosen case, we find that, in general, polydispersity inhibits
instabilities, increases the extent of the non percolating phase, and
diminishes the size of the gas-liquid coexistence region. We also consider the
first-order improvement of the mMSA (C0) closure (C1) and compare the
percolation and gas-liquid boundaries for the one-component system with recent
Monte Carlo simulations. Our results provide a qualitative understanding of the
effect of polydispersity on SHS models and are expected to shed new light on
the applicability of SHS models for colloidal mixtures.Comment: 37 pages, 7 figures, 1 tabl
Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion
Closed analytical expressions for scattering intensity and other global
structure factors are derived for a new solvable model of polydisperse sticky
hard spheres. The starting point is the exact solution of the ``mean spherical
approximation'' for hard core plus Yukawa potentials, in the limit of infinite
amplitude and vanishing range of the attractive tail, with their product
remaining constant. The choice of factorizable coupling (stickiness) parameters
in the Yukawa term yields a simpler ``dyadic structure'' in the Fourier
transform of the Baxter factor correlation function , with a
remarkable simplification in all structure functions with respect to previous
works. The effect of size and stickiness polydispersity is analyzed and
numerical results are presented for two particular versions of the model: i)
when all polydisperse particles have a single, size-independent, stickiness
parameter, and ii) when the stickiness parameters are proportional to the
diameters. The existence of two different regimes for the average structure
factor, respectively above and below a generalized Boyle temperature which
depends on size polydispersity, is recognized and discussed. Because of its
analycity and simplicity, the model may be useful in the interpretation of
small-angle scattering experimental data for polydisperse colloidal fluids of
neutral particles with surface adhesion.Comment: 32 pages, 7 figures, RevTex style, to appear in J. Chem. Phys. 1
December 200
Pathologies in the sticky limit of hard-sphere-Yukawa models for colloidal fluids. A possible correction
A known `sticky-hard-sphere' model, defined starting from a
hard-sphere-Yukawa potential and taking the limit of infinite amplitude and
vanishing range with their product remaining constant, is shown to be
ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an
{\it exact}second virial coefficient which {\it diverges}, unlike that of
Baxter's original model (SHS1). This deficiency has never been observed so far,
since the linearization implicit in the `mean spherical approximation' (MSA),
within which the model is analytically solvable, partly {\it masks} such a
pathology. To overcome this drawback and retain some useful features of SHS2,
we propose both a new model (SHS3) and a new closure (`modified MSA'), whose
combination yields an analytic solution formally identical with the SHS2-MSA
one. This mapping allows to recover many results derived from SHS2, after a
re-interpretation within a correct framework. Possible developments are finally
indicated.Comment: 21 pages, 1 figure, accepted in Molecular Physics (2003
Polydisperse fluid mixtures of adhesive colloidal particles
We investigate polydispersity effects on the average structure factor of
colloidal suspensions of neutral particles with surface adhesion. A sticky hard
sphere model alternative to Baxter's one is considered. The choice of
factorizable stickiness parameters in the potential allows a simple analytic
solution, within the ``mean spherical approximation'', for any number of
components and arbitrary stickiness distribution. Two particular cases are
discussed: i) all particles have different sizes but equal stickiness (Model
I), and ii) each particle has a stickiness proportional to its size (Model II).
The interplay between attraction and polydispersity yields a markedly different
behaviour for the two Models in regimes of strong coupling (i.e. strong
adhesive forces and low temperature) and large polydispersity. These results
are then exploited to reanalyze experimental scattering data on sterically
stabilized silica particles.Comment: 9 pages, 2 figures (included), Physica A (2001) to appea
Small Angle Scattering data analysis for dense polydisperse systems: the FLAC program
FLAC is a program to calculate the small-angle neutron scattering intensity
of highly packed polydisperse systems of neutral or charged hard spheres within
the Percus-Yevick and the Mean Spherical Approximation closures, respectively.
The polydisperse system is defined by a size distribution function and the
macro-particles have hard sphere radii which may differ from the size of their
scattering cores. With FLAC, one can either simulate scattering intensities or
fit experimental small angle neutron scattering data. In output scattering
intensities, structure factors and pair correlation functions are provided.
Smearing effects due to instrumental resolution, vertical slit, primary beam
width and multiple scattering effects are also included on the basis of the
existing theories. Possible form factors are those of filled or two-shell
spheres.Comment: 18 pages, 1 figure, uses elsart.st
Local orientational ordering in fluids of spherical molecules with dipolar-like anisotropic adhesion
We discuss some interesting physical features stemming from our previous
analytical study of a simple model of a fluid with dipolar-like interactions of
very short range in addition to the usual isotropic Baxter potential for
adhesive spheres. While the isotropic part is found to rule the global
structural and thermodynamical equilibrium properties of the fluid, the weaker
anisotropic part gives rise to an interesting short-range local ordering of
nearly spherical condensation clusters, containing short portions of chains
having nose-to-tail parallel alignment which runs antiparallel to adjacent
similar chains.Comment: 13 pages and 6 figure
Interaction of proteins in solution from small angle scattering: a perturbative approach
In this work, an improved methodology for studying interactions of proteins
in solution by small-angle scattering, is presented. Unlike the most common
approach, where the protein-protein correlation functions are
approximated by their zero-density limit (i.e. the Boltzmann factor), we
propose a more accurate representation of which takes into account
terms up to the first order in the density expansion of the mean-force
potential. This improvement is expected to be particulary effective in the case
of strong protein-protein interactions at intermediate concentrations. The
method is applied to analyse small angle X-ray scattering data obtained as a
function of the ionic strength (from 7 to 507 mM) from acidic solutions of
-Lactoglobuline at the fixed concentration of 10 . The
results are compared with those obtained using the zero-density approximation
and show a significant improvement particularly in the more demanding case of
low ionic strength.Comment: 12 pages, 3 figures, to appear in Biophysical Journal (April 2002)
Due to an unfortunate name mismatch, the original submission contained an
incorrect sourc
Patchy sticky hard spheres: analytical study and Monte Carlo simulations
We consider a fluid of hard spheres bearing one or two uniform circular
adhesive patches, distributed so as not to overlap. Two spheres interact via a
``sticky'' Baxter potential if the line joining the centers of the two spheres
intersects a patch on each sphere, and via a hard sphere potential otherwise.
We analyze the location of the fluid-fluid transition and of the percolation
line as a function of the size of the patch (the fractional coverage of the
sphere's surface) and of the number of patches within a virial expansion up to
third order and within the first two terms (C0 and C1) of a class of closures
Cn hinging on a density expansion of the direct correlation function. We find
that the locations of the two lines depend sensitively on both the total
adhesive coverage and its distribution. The treatment is almost fully
analytical within the chosen approximate theory. We test our findings by means
of specialized Monte Carlo (MC) simulations and find the main qualitative
features of the critical behaviour to be well captured in spite of the low
density perturbative nature of the closure. The introduction of anisotropic
attractions into a model suspension of spherical particles is a first step
towards a more realistic description of globular proteins in solution.Comment: 47 pages, 18 figures, to appear on J. Chem. Phy